What is the average value of e^x on the interval 3,9]

Name: What Is the Average Value of E^x on the Interval 3,9]
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Question

Answer 1

To find the average value of the function

on the interval

, we use the formula for the average value of a continuous function \( f(x) \) over the interval

:

In this case, \( f(x) = e^x \),

, and

. So, we need to compute:

First, compute the integral:

Now, substitute this result into the formula for the average value:

Thus, the average value of

on the interval

is:

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